# Find all points where the tangent line is horizontal: #x^2+xy+y^2=1#?

##### 1 Answer

POINTS:

#### Explanation:

We know the tangent line is horizontal when *on the curve* where

STEP 1: Use implicit differentiation to find

STEP 2: We are looking for where

STEP 3: Now we know that we have a horizontal tangent line whenever *the points on the curve* for which

STEP 4: When does

To solve this question, we can sub in

STEP 5: Now that we know the x-value of the point, we can easily find the y-value of the point because we know

POINTS: